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algebra senior

Problem

The expression

\frac{2 x ^{2} - x}{( x + 1 ) ( x - 2 )} - \frac{4 + x}{( x + 1 ) ( x - 2 )}

cannot be evaluated for

x = - 1

or

x = 2

, since division by zero is not allowed. For other values of

x

:

(A)

T h ee x p r ess i o n t ak eso nman y d i f f er e n t v a l u es .

(B)

T h ee x p r ess i o nha so n l y t h e v a l u e 2.

(C)

T h ee x p r ess i o nha so n l y t h e v a l u e 1.

(D)

T h ee x p r ess i o na l w a y s ha s a v a l u e b e tw ee n - 1 an d + 2.

Solution

\frac{2 x ^{2} - x}{( x + 1 ) ( x - 2 )} - \frac{4 + x}{( x + 1 ) ( x - 2 )} = \frac{2 x ^{2} - 2 x - 4}{( x + 1 ) ( x - 2 )}

This can be factored as

\frac{( 2 ) ( x ^{2} - x - 2 )}{( x + 1 ) ( x - 2 )} ⟹ \frac{( 2 ) ( x + 1 ) ( x - 2 )}{( x + 1 ) ( x - 2 )}

, which cancels out to

2 ⟹ The expression has only the value 2.

.

Final answer

B